Digital peak detector

ABSTRACT

A method and system for detecting the peak of respective half-cycles of a sinusoidal waveform. The sinusoidal waveform is rectified and only sample points above a first threshold are analyzed. The peaks of each half-cycle are only accepted if they are above a second, greater threshold. Peaks below the second threshold are not accepted. The peaks themselves are detected by starting a counter at the first sample in the rectified waveform which is above the first threshold value. Once the rectified waveform descends below the first threshold, the counter is stopped and the maximum value of the previous k samples is the peak value, where k is the counter value for the successive samples above the first threshold. The peak value so determined is rejected if it is less than the second threshold value. On the other hand, when the peak value is above the second threshold, it is averaged with the last valid peak value (above the second threshold). Thus, the V/Hz value remains the same until a new, valid peak is determined. A preferred embodiment implements such a digital peak detector in a digital relay system for detecting overexcitation of a power system.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. patent application Ser. No. 08/647,589, now U.S. Pat. No. 5,671,112 filed May 13, 1996, entitled "Digital Integrator V/Hz Relay for Generator and Transformer Over-Excitation Protection," the contents of which are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a technique for detecting peaks in a sinusoidal digital signal. In particular, the present invention provides a method and system for detecting peak values in sinusoidal digital signals having noise, harmonics and other disturbances therein.

2. Description of the Prior Art

Numerous systems and applications require identifying the peak value in a digitized sinusoidal signal. One such application is the Digital Integrator V/HZ Relay as described below and in parent U.S. patent application Ser. No. 08/647,589, now U.S. Pat. No. 5,671,112 entitled "Digital Integrator V/Hz Relay for Generator and Transformer Over-Excitation Protection." This technique may also be used in overvoltage and overcurrent detection systems and the like.

A problem often encountered in peak detection of a sinusoidal digital signal is the existence of noise or harmonics in the signal. The existence of noise greatly increases the difficulty of identifying a true peak value. As shown in FIG. 1, a rectified sinusoidal waveform has a smooth and consistent pattern. This smooth pattern lends itself to easily identifying the peak in each half-cycle of the signal. This same rectified sinusoidal waveform with noise and harmonics in the signal might appear as shown in FIG. 2. As shown, the noise and disturbances give the sinusoidal waveform an irregular and random shape which significantly increases the difficulty of detecting a true peak. For example, when detecting peak values, the peak values are often identified for each half cycle of a signal between zero crossing points 10 (FIG. 1). However, in a signal containing noise as shown in FIG. 2, often the signal values are artificially high and therefore have no zero crossing between half-cycles, as shown by points 12 and 14. This lack of zero crossing points complicates the process of detecting a peak value for each half cycle.

Also, as shown in FIG. 2, noise in the signal creates numerous small peak values, i.e., values which are greater than both the preceding and succeeding values. Such peaks, designated by reference numerals 16 and 18 in FIG. 2, are not true peaks in the signal. However, delineating between these artificial peaks and legitimate peak values is a not easily accomplished. It is difficult to determine whether a rise or fall in the sign wave is a true increase or decrease in the signal, or rather a random fluctuation due to noise or a harmonic. Thus, the random and artificial values associated with noise in a signal increase the difficulty of identifying a true peak. A technique is desired which identifies the true peak without falsely identifying local noise spikes as a peak.

As noted above, one system in which it is necessary to identify a peak for a digital signal is a digital integrator V/Hz relay. V/Hz relaying is conventionally used to protect generators and transformers from the damage caused by over-excitation, where the ratio of V/Hz is used as the measure of the generator's or transformer's over-excitation. As known to those skilled in the art, the excitation level of a generator or a transformer can be accurately measured by the ratio of the voltage magnitude over the frequency of a voltage impressed on them, thus the name V/Hz protection. Typically, the generator and transformer V/Hz protection function is required to work across the wide frequency range (5-80 Hz) which is experienced by a generator or a generator-transformer unit. Generally, a high V/Hz condition may occur during the start up or shut down of a generator when the speed of the generator is low and during a sudden load rejection or as a result of a certain system disturbance when the voltage suddenly becomes high while the frequency is only changed slightly or is not changed.

Conventional analog integrator type V/Hz relays (solid-state) can provide sufficient over excitation protection in the desired frequency range with high accuracy. The analog integrator can be viewed as a special type of low-pass filter with a frequency response characteristic that is inversely proportional to the input signal's frequency. As shown in FIG. 3, the basic circuit of an analog V/Hz relay is an analog integrator 90. Those skilled in the art will appreciate that the analog integrator 90 shown in FIG. 3 is not an ideal integrator, but that it becomes an ideal integrator if R₂ is infinite. This characteristic causes the integrator 90 to become unstable. However, by carefully selecting the values of the R₁, R₂ and C, the integrator 90 can approach the ideal integrator and still remain stable.

The transfer function of the analog integrator 90 of FIG. 3 is H(s)=A/(s-p), where A=-1/R₁ C and p=-1/R₂ C, and the frequency response of the integrator transfer function is obtained by substituting "s" with "jω", i.e.: ##EQU1##

Equation (2) shows that the magnitude of the output signal V_(o) from analog integrator 90 is proportional to the magnitude of the input signal V_(i) and inversely proportional to the frequency of the input signal, if ω>>p. For a practical circuit with R₁ =150 kΩ, R₂ =1 MΩ, and C=0.1 μF, its parameters are: A=-66.7 and p=-10. The actual |H(ω)| and ideal (|A|/ω) frequency response curves are plotted in FIGS. 4A and 4b and the relative error of |H(ω)| is plotted in FIG. 4c, where the relative error of |H(ω)| is defined as: ##EQU2##

As FIGS. 4A, 4b and 4c show, |H(ω)| and ideal (|A|/ω) are very close to each other. Thus, the analog integrator 90 can be used for V/Hz protection across a wide frequency range. In fact, the analog integrator 90 of FIG. 3 could work down to very low frequencies and still maintain an acceptable accuracy (relative error <0.5% from 20 Hz and up and relative error <4% from 5 Hz and up, for the above example). Such an integrator is always stable provided the real part of "p" is less than zero, which is the case in the above example.

From the above error equation, the smaller the value of |p| is, the smaller the relative error between |H(ω)| of the above analog integrator and the ideal (|A|/ω) is. However, since the transient response time constant of the circuit is T_(d) =|1/p|, the parameter p also determines the time delay of the circuit in response to a sudden change of the input signal. In the above example, the time constant is T_(d) =1/10=0.1 second, which is small. Thus, the parameter p could be chosen, such as in the above example, to obtain an |H(ω)| characteristic which is close to the ideal (|A|/ω) without introducing excessive transient response time delay.

Those skilled in the art will also appreciate that the analog V/Hz relay uses a peak-detection circuit to determine the peak value of the output signal of the analog integrator, which is representative of the V/Hz value, to implement the inverse time delay characteristic, or a level detect circuit when a fixed time delay characteristic is used. The present invention relates to an improved technique for determining the peak value of the output signal.

Digital V/Hz relay protection systems are generally known. For example, a prior art digital programmed overexcitation protective relay is described in U.S. Pat. No. 4,694,374 to Verbanets, Jr. The relay described by Verbanets, Jr. generates a first signal representative of the V/Hz value by integrating samples of a full cycle rectified voltage signal over a half cycle between two zero crossings using the trapezoidal or parabolic method or both. The first signal is then averaged over a predetermined period to generate a second signal, which is used to derive the time-to-trip for inverse time trip operation of the relay according to the disclosed method. The voltage signal used to compute the first signal is sampled at a predetermined fixed sampling frequency. Full cycle rectification circuits, zero-crossing detectors, and other special hardware are used to assist in the relay operation. The integration process of the half cycle sampled data is different depending on whether an even or odd number of samples is contained in the half cycle. A clean up procedure is applied to correct the error caused by the partial interval integration at the first and the last interval of a half cycle. Thus, in this relay, the first signal is a discrete signal which is output once in a half cycle, while the second signal is also a discrete signal which is output once in a predetermined period. However, the requirement of additional special hardware makes this type of V/Hz relay system less desirable.

The Discrete Fourier Transform (DFT) technique is conventionally used in digital protection systems to compute phasors of the input voltage and current signals for use by the different protection functions. To obtain an accurate DFT computation result, the samples used in the DFT computation must be taken from one fundamental cycle of the signal and be evenly spaced. If such sampling conditions are not met, the computed DFT phasors will be in error due to the well known spectrum leakage and picket fencing problems. In an integrated (multi-function) generator protection system using a DFT algorithm, the fundamental frequency of the voltage and current signals is not fixed but varies. As a result, the following techniques have to be used to compute the phasors correctly: (1) the sampling frequency is varied to keep a fixed number of samples per cycle which is equal to the fixed number of data points used in the DFT computation; or (2) the sampling is conducted at a fixed frequency but the DFT window length is varied to keep the number of data points used in the DFT computation equal to the number of samples in one cycle. In the varying sampling frequency approach, the frequency of the input voltage, which is used to dynamically change the sampling frequency, is obtained as the result of frequency tracking. In the varying DFT window approach, on the other hand, the frequency of the input voltage, which is used to change the DFT window length, is obtained as the result of frequency estimation using the DFT phasor angle difference.

The computation of the V/Hz value in an integrated digital generator protection system using either of the above-mentioned DFT-based techniques appears to be relatively straightforward, since on its face all that is required is dividing the measured voltage by the measured frequency. However, this approach cannot provide an accurate V/Hz measurement in the desired operating frequency range of a V/Hz relay as the frequency approaches zero, for neither of the two above-mentioned techniques are suitable at low frequencies due to aliasing (the need of a very low cutoff frequency filter), the response time (the need to wait for one cycle of data to become available), and other problems. If the anti-aliasing is not performed properly, errors will occur in the phasor computation according to the well-known Nyquist Theorem. To avoid such aliasing problems, the sampling frequency must be fixed at the value corresponding to the low frequency limit of the varying sampling frequency approach when the actual frequency is below that limit, or the DFT window length must be fixed at the length corresponding to the low frequency limit in the varying DFT window length approach when the actual frequency is below the limit. Unfortunately, even with such anti-aliasing measures applied, the phasor computation and the frequency estimation still contain errors for both DFT techniques when the actual frequency is below the low frequency limit established by the Nyquist Theorem, for the DFT is no longer performed on samples in a single cycle. Consequently, the V/Hz value computed using the voltage phasor and the estimated frequency is inaccurate when the actual frequency is below the low frequency limit, which may occur during a generator's start-up and shut-down process when its speed is low.

Unlike the V/Hz relay, most of the generator protection functions are only required to operate when a generator is running around its nominal speed. The operating frequency range provided by the varying sampling frequency approach or the varying DFT window length approach is thus sufficient for the correct operation of these protection functions. It would be advantageous for an integrated generator protection system to use DFT techniques for these functions while using other techniques to perform a more accurate V/Hz protection function and other protection functions which are required to operate in a much wider frequency range so that overall better system performance can be achieved. As will be described in detail below, the relay system described herein which implements the preferred embodiment of the digital peak detector of the present invention has been designed to address this problem for fixed and variable sampling frequencies by directly computing an accurate V/Hz ratio from the sampled input voltage signal so that the results are similar or improved in comparison with the prior art analog circuit of FIG. 3.

Since the relay system incorporating the digital peak detector of the present invention uses digital samples for the V/Hz trip determination, the relay system is obviously different from an analog V/Hz relay using an analog integrator where both input and output signals are continuous signals. As will also be appreciated from the following detailed description, such a relay system further differs from the DFT based V/Hz relaying technique where the value of V/Hz is obtained by dividing the voltage magnitude by the frequency computed separately from the DFT and the frequency estimation technique in that the ratio of V/Hz of the sinusoidal input signal is obtained directly. In addition, the relay system described herein as incorporating the preferred embodiment of the digital peak detector of the present invention differs from the programmed overexcitation protective relay taught by Verbanets, Jr. since Verbanets, Jr. uses a non-recursive digital integration method supported by special hardware for the derivation of the V/Hz values by integrating samples of a full cycle rectified voltage signal over a half cycle between two zero crossings using trapezoidal or parabolic methods, or both. The integrated generator protection system of the relay system herein described does not require such additional hardware support for the V/Hz relay. Instead, the relay system described herein uses the same voltage samples as used by the above-mentioned DFT techniques to perform V/Hz relaying in the desired operating frequency range and operates independently regardless of the sampling frequency approach (fixed or varying) being used in the system. Details of the implementation of the invention will be provided in the following detailed description.

SUMMARY OF THE INVENTION

A digital peak detection technique in accordance with the present invention overcomes the difficulties associated with prior art digital peak detection techniques by only analyzing sample points above a certain threshold and only accepting sample points as valid peaks if they are above a second, higher threshold. When a peak is above the higher threshold, and hence valid, it is averaged with the last valid peak value and the thresholds are adjusted.

In particular, the inventive method of detecting a peak in a sinusoidal digital signal in accordance with the invention comprises the steps of: establishing a first threshold which is a first predetermined percentage of the magnitude of the sinusoidal digital signal; establishing a second threshold which is a second predetermined percentage of the magnitude of the sinusoidal digital signal, the second threshold being greater than the first threshold; counting each successive sample in the half-cycle of the sinusoidal digital signal above the first threshold; determining which sample k counted in the counting step had the greatest magnitude; comparing a magnitude of sample k to the second threshold; and rejecting sample k as the peak of the sinusoidal digital signal if the magnitude of sample k is less than the second threshold. On the other hand, if the magnitude of sample k is greater than the second threshold, the magnitude of sample k is saved as a valid peak value and averaged with the last valid peak value of a previous half-cycle of the sinusoidal digital signal.

In accordance with the invention, a typical value for the first threshold is preferably in the range of approximately 10-30% of the magnitude of the last valid peak value of a previous half-cycle of the sinusoidal digital signal, while the second threshold is preferably approximately 40-60% of the magnitude of the last valid peak value of a previous half-cycle of the sinusoidal digital signal.

Generally, a peak detector system in accordance with the present invention is implemented using an analog to digital converter for generating a sinusoidal digital signal; a digital rectifier which rectifies the amplitude of the sinusoidal digital signal; and a processor programmed with software to identify the peak value in the sinusoidal digital signal by comparing the magnitudes of the samples to the first and second thresholds as described.

A preferred embodiment of a such a peak detector is preferably implemented in a Digital Integrator type V/Hz relay which obtains the ratio of V/Hz of a sinusoidal input signal directly. Digital Integrator type V/Hz relaying techniques as described herein are based on the integration of an input sinusoidal signal x=B sin(2πft) (where f is the frequency of x, B is the amplitude of x, and t is time): ##EQU3## As can be seen from the above equation, the magnitude of the integrated output signal y is inversely proportional to the frequency of the input signal x. Accordingly, the peak value of the integrated signal calculated in accordance with the invention can be used to obtain the required V/Hz ratio.

The preferred Digital Integrator relay which employs the peak detection technique of the invention is a programmed protective relay system for protecting power equipment, supplied with energy from at least one power line, against overexcitation by generating an overexcitation relay signal and providing the relay signal to a circuit breaker which separates the power equipment from a source of the overexcitation. In one embodiment, the relay system comprises a voltage sensor for sensing a voltage of one or more power lines, frequency determining means for determining a frequency of the sensed voltage of the one or more power lines, analog to digital conversion means for sampling and digitizing the sensed voltage at a sampling frequency so as to form a digital voltage signal, a digital integrator for integrating the digital voltage signal in a manner independent of the sampling frequency, and processing means for calculating a voltage/frequency ratio of the power line(s) from a peak magnitude of an output of the digital integrator determined using the technique of the invention and the frequency determined by the frequency determining means. The relay signal is then generated when the voltage/frequency ratio exceeds a predetermined operating condition value.

The digital integrator of the relay system is comprised of a digital filter having filter coefficients directly linked to the desired frequency response characteristic and the sampling frequency. The filter coefficient equations are obtained from the transfer function of the analog integrator using the difference equation mapping method. The digital integrator's filter coefficients can be recalculated and adjusted on-line each time the sampling frequency is changed to maintain a desired frequency response characteristic when the varying sampling approach is used. The filter coefficients are adjusted according to the actual sampling period at the time when the samples are taken. The digital integrator is then applied to the voltage samples to generate a first signal each time a sample is received, and the first signal is then digitally rectified to produce a second signal. The peak values of the second signal representative of the accurate V/Hz values are detected using the digital peak detector of the invention and used together with the digitally rectified second signal to generate V/Hz relaying signals.

The digital filter of the digital integrator processes samples of the input voltage signal x directly from the above equation, where x=B sin(2πft), "B" is the magnitude of the voltage signal, "f" is the frequency of the voltage signal, and "t" is time. One of the coefficients, i.e., the one which is to multiply with the previous time step's digital integrator's output, must be less than one to ensure that the digital integrator is stable. However, those skilled in the art will appreciate that this is the case when the digital integrator is designed using the difference equation mapping method described herein.

In accordance with another aspect of the digital integrator relay, the ratio-frequency characteristics of the voltage sensor and/or the digital integrator may be measured and stored, and then used with the fundamental frequency value measured on-line by other techniques to correct the nonlinear frequency response characteristics of the voltage sensors and/or to correct the non-ideal characteristics of the digital integrator.

Thus, the V/Hz ratio is computed by performing the steps of sensing a voltage of one or more power lines, determining a frequency of the sensed voltage of the one or more power lines, sampling the sensed voltage at a sampling frequency so as to form a digital voltage signal, digitally integrating the digital voltage signal using a digital integrator in a manner independent of the sampling frequency, measuring a peak magnitude of an output of the digital integrator from the fully-rectified waveform as described above, and calculating a voltage/frequency ratio of the one or more power lines from the peak magnitude and the frequency determined in the frequency determining step. An overexcitation relay signal is then generated when the voltage/frequency ratio exceeds a predetermined value, and the relay signal is provided to a circuit breaker which separates the power equipment from a source of the overexcitation. For systems with variable sampling frequencies, the digital integrator's filter coefficients are adjusted when the sampling frequency is changed, and the sampled voltage signal is passed through the digital integrator with the adjusted filter coefficients. The new peak value of the digital integrator's output is then measured using the inventive method and system for peak detection. As in fixed sampling frequency systems, the computed V/Hz value is compared with predetermined settings to generate the relay signals.

The technique of the invention can be used in a digital system using either a fixed sampling frequency or a variable sampling frequency. Preferably, if the sampling frequency is variable, the filter coefficients of the digital integrator are recalculated each time the sampling frequency is changed, where at least one of the filter coefficients is less than one so that the digital integrator is stable.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects and advantages of the invention will become more apparent and more readily appreciated from the following detailed description of presently preferred exemplary embodiments of the invention taken in conjunction with the accompanying drawings, of which:

FIG. 1 illustrates a simple rectified sinusoidal signal such as an alternating current signal.

FIG. 2 illustrates a rectified sinusoidal signal such as an alternating current signal with noise and other disturbances therein.

FIG. 3 illustrates a conventional analog integrator circuit.

FIGS. 4A and 4b together illustrate a comparison of the frequency response curves between an ideal and an actual analog integrator circuit of the type illustrated in FIG. 3.

FIG. 4c illustrates the relative error between an actual analog integrator circuit and an ideal integrator circuit of the type illustrated in FIG. 3.

FIG. 5 illustrates a multi-function digital generator protection unit for measuring an overexcitation condition of a generator or transformer in accordance with the techniques of the relay system described herein.

FIGS. 6(a) and 6(b) respectively illustrate the main and sample interrupt software routines implemented on a processor of the DSP sub-system 109.

FIG. 6c is a flow chart illustrating the V/Hz value computation by the DSP software in accordance with the techniques of the digital relay described herein.

FIGS. 6D-6G illustrate the signals generated at different stages of the digital integration V/Hz value calculation in accordance with the digital relay described herein.

FIG. 7 illustrates a lower and upper threshold positioned on a rectified sinusoidal digital signal such as an alternating current signal with noise and other disturbances therein.

FIG. 8 is a logical flowchart of a preferred embodiment of the peak detecting technique in accordance with the invention.

FIG. 9 is a block diagram of the peak detection system of the invention.

FIGS. 10(a) and 10(b) respectively illustrate the main and protection function software routines implemented on a processor of the CPU sub-system 110.

FIG. 10C is a flow chart illustrating the instant trip and delayed trip time calculations using the V/Hz values calculated in accordance with the techniques of the relay described herein.

FIGS. 11A and 11B illustrate the frequency response of the digital integrator of the relay described herein.

FIG. 12 illustrates the "peak-miss" error at different sampling frequencies for the desired frequency range of the digital integrator of the relay described herein.

FIG. 13 illustrates a frequency range comparison between the varying sampling frequency approach used in a conventional relay (30.5-79.5 Hz) and the V/Hz relay described herein (5-80 Hz).

FIG. 14 illustrates a frequency range comparison between a varying DFT window technique (16.8-87.3 Hz) and the V/Hz relay as described herein (5-80 Hz).

DETAILED DESCRIPTION OF PRESENTLY PREFERRED EMBODIMENTS

A method and system of peak detection with the above-mentioned beneficial features in accordance with a presently preferred exemplary embodiment of the invention will be described below with reference to the various Figures of the drawing. It will be appreciated by those of ordinary skill in the art that the description given herein with respect to those figures is for exemplary purposes only and is not intended in any way to limit the scope of the invention. All questions regarding the scope of the invention may be resolved by referring to the appended claims.

As shown in FIG. 5, the present invention is preferably, though not necessarily, implemented in a system containing a multi-function digital generator protection unit (GPU) 100 which is designed to protect a generator/step-up transformer set 101. As known by those skilled in the art, GPU 100 controls the main breaker 104 to connect and disconnect generator/transformer set 101 to/from the main AC system. GPU 100 may also control the field breaker 103 to connect and disconnect the generator excitation voltage supply 102 to/from the generator field winding of the generator/transformer set 101. In short, GPU 100 detects those conditions requiring control, alarm and shut down of an associated generator/transformer, and upon detection of an overexcitation condition of the associated generator, an instant or delayed trip of the generator field circuit breaker and/or main circuit breaker is initiated via external interfaces of GPU 100.

The GPU 100 functions by converting the three phase currents and voltages of the generator/transformer set 101 from the actual signals to appropriate current and voltage signals using current sensors 105 and voltage sensors 106, respectively. The output signals of current sensors 105 and voltage sensors 106 are then sampled using a predetermined sampling frequency approach (fixed or variable) and converted from analog to discrete digital signals by sample/hold & A/D conversion sub-system 107. The voltage signals are also used by the frequency measurement circuit 108 to measure the fundamental frequency of the voltage using known methods.

For example, the frequency may be measured in the frequency measurement circuit 108 by first filtering the input voltage signal using an analog bandpass or lowpass filter. The cutoff frequency could be set equal to the fundamental frequency of the voltage signal to filter out noises and harmonics. The sinusoidal output signal of the filter is then converted into a square waveform and the width of the square waveform is measured by a high frequency pulse using a digital counter and read into the DSP sub-system 109. The fundamental period T (=1/f) can be computed from the number of pulses counted in one cycle and the pulse length of the high frequency pulse. The measured frequency is then used for frequency related protection functions, such as over-frequency and under-frequency excitation protection, and may also be used to compensate nonlinear frequency response characteristics of the voltage sensors 106 and/or the non-ideal characteristics of the digital integrator applying well known table look-up or curve-fitting methods.

Voltage sensors 106 may have a nonlinear voltage transfer ratio over the desired V/Hz frequency range, which causes additional errors in the V/Hz relay determination. Accordingly, the ratio-frequency characteristic of a particular voltage sensor can be measured and stored in the relay for correcting the errors caused by the voltage sensors 106.

The digitized and sampled data are processed in Digital Signal Processor (DSP) sub-system 109 to generate DFT phasors, RMS values, V/Hz values, and the like of the sampled signals for use by different protection functions implemented in software on Central Processing Unit (CPU) sub-system 110. The CPU sub-system 110 further interfaces with a front panel controller 111 to display data and waveforms on LED and LCD display 112 and to read data from keyboard 113 and with communication channels 114 to communicate with local and remote computers for data exchange. The CPU sub-system 110 may also interface with output contacts 115 to send out alarm signals and trip signals to trip breakers such as breakers 103 and 104 and with input contacts 116 to obtain additional information used by some protection functions of the CPU sub-system 110. All components of GPU 100 receive their power supply from power supply 117.

The software of GPU 100 is divided into three parts: one for the DSP sub-system 109, one for the CPU sub-system 110, and one for the front panel controller 111. Since the software for the front panel controller 111 performs conventional functions such as inputting settings, displaying results, and the like, it will not be described in detail. The functioning of the portions of the DSP software and CPU software related to the V/Hz relaying function and the digital peak detection in accordance with the invention will now be described with respect to FIGS. 6-10.

The DSP software implemented on DSP sub-system 109 controls sample/hold & AID conversion circuit 107 and processes the sampled data to generate DFT phasors, RMS values, V/Hz values, and the like for use by the protection functions of the CPU sub-system 110. The processing of the sampled data is performed each time that new samples of voltages and currents are obtained during each sampling interval.

FIGS. 6(a) and 6(b) show the overall DSP sub-system software flow chart, while FIG. 6c shows the flow chart related to V/Hz value computation in step 206 of the DSP software shown in FIG. 6(b). As illustrated in FIG. 6(a), the DSP program starts at step 201 and performs initializations of the DSP hardware of DSP sub-system 109 and the DSP software on a processor of DSP sub-system 109 at step 202. The main program of FIG. 6(a) loops forever at step 203 to perform the background functions until a sample interrupt is received. Then, when a sample interrupt is received, the subroutine of FIG. 6(b) is entered at step 204. Upon entry of the sample interruption subroutine, the current and voltage signals from current sensors 105 and voltage sensors 106 are sampled by sample/hold & A/D conversion circuit 107 at step 205. The DFT phasors, RMS values, V/Hz computations and the like are then performed at step 206 before the sample interruption subroutine is exited at step 207. The computation of the DFT phasor and the RMS values do not form part of the invention and may be computed using conventional DFT techniques. Calculation of the V/Hz values now be described with respect to FIG. 6c.

As shown in FIG. 6c, the V/Hz value computation is performed in the DSP software by entering the V/Hz calculation program at step 301. In order to perform the new V/Hz value computation, the sampling period Δt (=1/f_(smp), where f_(smp) is the sampling frequency), the new voltage sample x_(k), and the new frequency "f" measured by the frequency measurement circuit 108 are read in at step 301. The new values of the filter coefficients "a" and "b" are computed at step 302 using Δt (described in more detail below) if the sampling frequency has changed. Thus, unlike prior art relaying systems which require the sampling frequency to remain constant, the present relay system accommodates dynamic sampling frequency changes by recalculating the filter coefficients "a" and "b" at each sampling interval. A new output value y_(k) is then calculated at step 303 using the digital integration techniques of the invention (described in more detail below), and the new voltage sample x_(k) and the resulting values y_(k) and y1_(k) (=|y_(k) |) are stored at step 304 for use by the process in the next sampling interval by the CPU software. The frequency compensation for the voltage sensors 106 and the digital integrator may be performed at step 304 on y1_(k) before it is stored. Then, at step 305, y2_(k) (=|y1_(k-1) |) is stored as a new V/Hz value if it is a peak, as determined in accordance with the techniques of the invention described below with reference to FIGS. 7-9. The V/Hz calculation program is then exited at step 306.

FIGS. 6D-6G show the signals at each processing stage of the digital integrator relay. Signal 307 is the sampled input voltage signal, which corresponds to x_(k) in step 303 of FIG. 6C and could be sampled at either a fixed frequency or a varying frequency. Signal 308 is the output y_(k) of the digital integrator in step 303 of FIG. 6C, which still has a sinusoidal envelope. Signal 308 is y1_(k) obtained in step 304 in FIG. 6C, which is the rectified digital integrator output y_(k). Signal 310 (y2_(k) in step 305 of FIG. 6c) is the V/Hz value computed by detecting the peak value of signal 309 using the peak detection techniques of the invention. As will be described below, signal 309 (y1_(k)) is then used in step 503 of FIG. 10C for instant trip determination, and the signal 310 (y2_(k)) is used in step 505 of FIG. 10C for computing the time-to-trip if it exceeds the pick-up level.

As just noted, signal y2_(k) in step 305 of FIG. 6c is the V/Hz value computed by detecting the peak value of signal 309 and is used for instant trip determinations. In accordance with a preferred embodiment of the peak detection technique of the invention, the maximum amplitude of each half cycle is determined as described below with respect to FIGS. 7-9.

In accordance with the peak detection technique of the invention, the detection of the maximum amplitude of a half-cycle of the rectified sinusoidal signal (signal 309 in FIG. 6F) is simplified by only analyzing sample points above a certain threshold and only accepting the peaks if they are above a second, greater threshold. Peaks below the second threshold are not accepted. Peaks themselves are detected by starting a counter at the first sample in the rectified waveform (signal 309) which is above the first threshold value. Once the rectified waveform descends below the first threshold, the counter is stopped and the maximum value of the previous k samples is the peak value, where k is the counter value for the successive samples above the first threshold. The peak value so determined is rejected if it is less than the second threshold value. On the other hand, when the peak value is above the second threshold, it is averaged with the last valid peak value (above the second threshold). Thus, the V/Hz value remains the same until a new, valid peak is determined.

The first threshold value serves two functions: filtering out "peaks" which are obviously the result of noise and harmonics, and insuring that each half cycle is appropriately distinguished from succeeding half-cycles. FIG. 7 provides a graphical depiction of a rectified sinusoidal signal with noise therein. The horizontal lines across the signal represent the first threshold 20 and the second threshold 22. Signal values below the first or lower threshold 20, which although they may be a peak, i.e., higher than the reading immediately before and immediately after, are due to noise and disturbances and therefore are not considered legitimate peak values. Thus, the first or lower threshold 20 is employed to filter out obviously non-legitimate peak values.

Optimally, a peak value is identified for each half-cycle beginning and ending at a zero crossing. However, as shown in FIG. 7, for a signal containing noise and harmonics, it is likely portions of the signal may be artificially high. As a result, and as shown, there may be no zero crossing at minimums 24 and 26 between the half cycles, thereby making it difficult to distinguish successive half cycles. The technique of the invention accounts for artificially high signal values and the lack of a zero-crossing by equating a crossing of the lower threshold 20 with a conventional zero crossing. Thus, the beginning or end of a half-cycle is identified by a lower threshold 20 crossing so as to compensate for artificially high sample values due to signal noise.

In the preferred embodiment, the lower threshold 20 ranges from 10-30% of the output peak from the previous half cycle. The present inventors have determined that a lower threshold 20 set at 10-30% of the previous peak is sufficiently low to identify clearly non-legitimate peak values which may be caused by noise and harmonics. Further, the present inventors have determined that this range is sufficiently high to account for artificially high minimum values in the waveform for purposes of distinguishing one half-cycle from a succeeding half-cycle. Also, the present inventors have observed that for a signal with a high sampling rate, a lower threshold 20 in the lower part of the 10-30% range of the previous peak is most effective, while, for signals having a lower sampling rate, a threshold 20 in the higher part of the 10-30% range of the previous peak is most effective depending upon the amount of signal noise.

After a peak value which rises above the lower threshold 20 has been identified for a particular half-cycle, the identified peak is compared to a second or upper threshold 22 to further clarify if it is a valid peak. The second threshold 22 operates to eliminate signal values that simply are not high enough to be a true peak value and is preferably approximately twice the first threshold. Applicants have determined that a threshold of 40-60% of the previous peak is effective in identifying legitimate peak values depending upon the amount of noise.

If a peak value in a half-cycle is greater than the higher or second threshold 20, it is determined to be a legitimate peak value for that half cycle. This legitimate peak value is then averaged with the last previously identified valid peak from the preceding half-cycle. Averaging the values minimizes the effect of DC offset and odd harmonics errors on the output peak value. This averaged value is the peak value which is output for use in the relay protection function described in detail below.

FIG. 8 provides a detailed logical flow chart of the peak detection technique of the invention which, in a preferred embodiment, is implemented in software on a microprocessor of DSP sub-system 109. As shown, at step 30 values consistent with the expected peak value are assigned to several variables including those used for storing the output peak value, the previous peak value from the succeeding half cycle, a lower threshold and an upper threshold. These variables must be initialized for the first iteration of the process. At step 32, a counter variable and a variable for storing the highest peak in the current half cycle reading are initialized to zero.

At step 34 a rectified signal waveform is read into memory. At step 36, the system checks whether the signal value is above the lower threshold. If so, the counter is incremented at step 38. Thereafter, at step 40 the system checks for whether the most recently established peak for the half-cycle of the signal is greater than the current sample signal value. If the current peak for the half-cycle is greater than the current sample signal value, indicating that the current sample is not a peak, the system returns to step 34 where the next signal value is read. However, if the current peak is not greater than the current sample, a new current peak value for the half-cycle has been identified. The system thus sets the current peak value equal to the magnitude of the current sample at step 42 and returns to step 34 where the next signal value is read.

On the other hand, if at step 36 it is determined that the current sample signal value is not greater than the lower threshold, at step 44 the system checks whether the counter is greater than zero. If the counter is not greater than zero, indicating that the previously read signal value also was not above the minimum threshold, the system returns to the operation of reading the next signal value at step 34. However, if the counter is greater than zero, indicating that at least one previously read signal was above the lower threshold, at step 46 the system checks whether the current peak value for the half cycle is greater than the upper threshold. If the current peak value for the half cycle is not greater than the upper threshold, then the peak value is ignored and the system initializes at step 32 for the next half-cycle. On the other hand, if the current peak value is greater than the upper threshold, indicating that a new legitimate peak value has been identified, at step 48 the system sets the output peak value as the average of the current peak value and the previous peak value from the succeeding half-cycle. At step 50, the lower and upper thresholds are recalibrated in relation to the new output peak value. As a result of this recalibration, if the peaks of the output waveform oscillate, then the first and second threshold values will also oscillate. Finally, at step 52 the new output peak value is output from the peak detection process system and control returns to the initialization step 32.

A typical peak detection system in accordance with the present invention is depicted in FIG. 9. As shown, a peak detection system 54 in accordance with the present invention comprises an analog to digital converter 60 which receives an input signal from a signal generator 59, such as sensors 105 and 106 in FIG. 5. The digital signals from the analog to digital converter 60 may undergo various forms of pre-processing in pre-processing block 62 to determine various characteristics of the digital signal such as frequency. The pre-processed signal is then rectified by rectifier 64, and the digital rectified signal is sent to a processor 66 which executes the steps described above to identify a peak value. The identified peak value is then output to another sub-system 68. Of course, in the preferred embodiment of the peak detection system of the invention, sub-system 68 is the digital integrator relay as described herein.

The software of CPU 110, on the other hand, controls the communication channels 114 and output contacts 115, reads the status of the input contacts 116, performs all designed protection functions for the generator/transforner set 101, and, at the same time, the CPU software interfaces with the front panel controller 111 to read data from the keyboard 113 and to display data and waveforms on the front panel's LEDs and LCDs. A simplified flow chart of the CPU sub-system software is shown in FIGS. 10(a) and 10(b), and the related flow chart for the V/Hz relay function (block 405 in FIG. 10(b) is shown in FIG. 10C.

As illustrated in FIG. 10(a), the CPU program starts at step 401 and performs initializations of the CPU hardware of CPU sub-system 110 and the CPU software on a processor of CPU sub-system 110 at step 402. The main program of FIG. 10(a) loops forever at step 403 to perform designated protection functions as well as other tasks. When a protection function is to be performed, the protective function subroutine of FIG. 10(b) is entered at step 404. The V/Hz relay functions are performed at step 405 in a conventional manner in dependence upon the V/Hz values calculated in the DSP sub-system software (FIG. 6c). For example, a "trip" signal may be sent to breakers 103 and/or 104 if an overexcitation condition is detected. Other generator/transformer set 101 protection functions are then performed at step 406 before the protection function subroutine is exited at step 407.

Each time the protection function subroutine of FIG. 10(b) is executed, the V/Hz relay function of step 405 is entered at step 501 (FIG. 10C) to check to see if the instant y1_(k) value from the DSP sub-system 109 (signal 309 of FIG. 6F) exceeds the preset instant trip level when the instant trip of V/Hz is enabled (blocks 502 and 503 of FIG. 10C). A trip signal will be generated at step 503 immediately if the preset level is exceeded. For a V/Hz relay delayed trip function, on the other hand, the system operates according to the selected generator/transformer capability curve in accordance with known techniques. In other words, if it is determined at step 504 that a new V/Hz value y2_(k) is obtained (signal 310 of FIG. 6G), then the time-to-trip (either fixed or inverse time delay) is computed at step 505 when the new y2_(k) value exceeds the preset pick up level. If the pick up level is exceeded, the inverse time trip signal is then sent out at step 506 at the end of the time delay. The time to trip is then reset based on the cooling factor of the generator/transformer set 101, and the V/Hz relay function is exited at step 507.

As noted above, the digital relay described herein is primarily directed to a new method of implementing accurate V/Hz value measurement and trip time determination for generator/transformer overexcitation protection in a manner which is independent of the conventional frequency tracking and phasor estimation based on Discrete Fourier Transformation (DFT) techniques in a multi-function GPU 100 of the type described above with respect to FIGS. 5, 6, and 10. The digital relay uses the same sampled data as are used by the DFT technique for other functions, but does not use any phasor estimation results of the DFT technique. Instead, the V/Hz ratio is computed directly from the sampled voltage data using the techniques described below. The result is overall better performance for the digital GPU system.

In particular, the V/Hz ratio is computed by passing the sampled voltage signal through a digital integrator and measuring the magnitude of the digital integrator's output. Preferably, the digital integrator is implemented in the DSP software (FIG. 4c) of DSP sub-system 109 in place of the conventional algorithm for tracking the frequency and estimating the voltage phasors. Such a technique avoids the computation of voltage magnitude and obtains an accurate V/Hz ratio directly from the sampled voltage data. As will be appreciated by those skilled in the art, this technique can be used in a digital system using either a fixed or a variable sampling frequency.

The Digital Integrator type V/Hz relaying techniques obtain the ratio of V/Hz of a sinusoidal input signal directly. The Digital Integrator type V/Hz relaying techniques are based on the integration of an input sinusoidal signal x=B sin(2πft) (where f is the frequency of x, B is the amplitude, and t is time): ##EQU4## As can be seen from the above equation, the magnitude of the integrated output signal y is inversely proportional to the frequency of the input signal x. Thus, the peak value of the integrated signal can be used to obtain the required V/Hz ratio.

The Digital Integrator type V/Hz relaying technique is designed using a difference equation mapping method, that is, the analog integrator 90 shown in FIG. 3 is implemented in a digital system as a difference equation. The design method employed in the digital integrator type relay provides a direct link between the coefficients of the digital integrator and the sampling period as well as the parameters A and p of the familiar analog integrator's transfer function H(s)=A/(s-p), which offers several advantages to the digital integrator type V/Hz relaying techniques as will be described in more detail below.

The differential equation for the analog integrator of FIG. 3 is: ##EQU5## If x=Vi(t) and y=Vo(t), then ##EQU6## Equation 6 can be rewritten as: ##EQU7## Equation 6a can be differentiated in different ways to provide a Digital Integrator type V/Hz relaying technique. For example:

1. Simple voltage difference ("Running Sum" Digital Integrator V/Hz relaying technique): ##EQU8## where Δt is the sampling period (=1/f_(smp), where f_(smp) is the sampling frequency), which leads to

    y.sub.k =ax.sub.k +by.sub.k-1                              Equation (8)

where ##EQU9##

2. Center difference ("Trapezoid Rule" Digital Integrator V/Hz relaying technique): ##EQU10## where Δt is the sampling period (=1/f_(smp), where f_(smp) is the sampling frequency), which leads to

    y.sub.k =a(x.sub.k +x.sub.k-1)+by.sub.k-1                  Equation (11)

where ##EQU11##

Those skilled in the art will appreciate that the Digital Integrator type V/Hz relaying techniques just described are recursive type digital algorithms which may be preferably implemented as software on a processor of the DSP sub-system 109 of GPU 100. Those skilled in the art will also appreciate that the coefficient "b" of the algorithm must be less than 1 in order for the algorithm to be stable. One of the advantages of the above method is that the stability of the algorithm is ensured if a "p" less than zero (as with the stable analog integrator) is used. Since the parameter "p" of the transfer function H(s)=A/(s-p) also determines the frequency response characteristic and the transient response time, those skilled in the art will appreciate that, using Equations (9) or (12), a digital integrator can be easily designed to have the desired frequency response characteristic and transient response time. The frequency response of a resulting digital integrator using the same "A" and "p" values of the exemplary analog integrator is illustrated in FIGS. 11A and 11B, which are quite similar to the corresponding curves in FIGS. 4A and 4b for the analog integrator 90 of FIG. 3.

A peak detector in accordance with the present invention is needed to determine the peak of the sinusoidal output of the digital integrator each half cycle, and such an implementation is a preferred implementation. Those skilled in the art will also appreciate that when the peak detector of the invention is implemented in a digital system, the Digital Integrator type V/Hz relaying techniques described herein will have a "peak-miss" error in detecting the actual peak of the integrated signal. The "peak-miss" error is caused by the fact that the actual peak of the integrated signal may appear in between two discrete sample points. The maximum error will occur when the actual peak is at the mid-point of two output points y_(k) and y_(k-1). Assuming the sampling frequency is "f_(smp) ", and the input signal's frequency is "f", then the maximum "peak-miss" error will be: ##EQU12##

The "peak-miss" error at different sampling frequencies for the desired V/Hz frequency range is shown in FIG. 12. Analysis of Equation 13 shows that a sampling frequency higher than 1920 Hz for the fixed sampling frequency approach or 24 samples/cycle for the varying sampling frequency approach will be sufficient to reduce this error to below 0.1% across the desired V/Hz frequency range (5-80 Hz).

As will be appreciated by those skilled in the art, the coefficients of the digital integrators are directly linked to the sampling period (or sampling frequency) of the digital system. As a result, the digital integration technique described herein can be used either for a fixed sampling frequency approach or for a variable sampling frequency approach. If the variable sampling approach is used, the coefficients of the digital integrators can be computed every time the sampling frequency is updated to maintain the desired frequency response characteristic.

The digital integration technique thus provides for improved V/Hz relaying using digital integration in an otherwise DFT based multi-function relay system. In other words, the present inventors recognize that the DFT technique may be suitable for most of the generator protection functions when a variable sampling frequency technique plus fixed DFT window technique is used or a fixed sampling frequency technique plus varying DFT window technique is applied, for most of generator protection functions are only required to operate around the rated frequency (60 Hz in North America). For both techniques, their covered frequency range is determined by the anti-aliasing limitation at the low frequency end and the computation power limitation at the high frequency end. Unlike in a stand-alone protection system where the system hardware and the software can be designed to meet the specific requirements of a particular function, the sampling frequency approach (either varying or fixed) and/or the DFT technique used in such a system is usually determined by the overall system requirements but not an individual function. However, since the frequency range provided by the DFT technique does not meet the V/Hz relay's requirements, the relay techniques as described herein is very useful in providing adequate V/Hz relaying in a DFT technique based multi-function generator protection system.

FIG. 13 illustrates a frequency range comparison between the varying sampling frequency approach used in a conventional General Electric relay (30.5-79.5 Hz) and the V/Hz relay described herein (5-80 Hz), while FIG. 14 illustrates a frequency range comparison between a varying DFT window technique (16.8-87.3 Hz) and the V/Hz relay described herein (5-80 Hz).

Thus, the main advantages of the Digital Integrator type V/Hz relaying technique are: (1) The Digital Integrator type V/Hz relaying technique can be easily designed to have the desired frequency response characteristic and the desired transient response delay time. (2) High accuracy across the desired V/Hz relaying frequency range (5-80 Hz) is obtainable. (Indeed, the relative error for the example is less than 0.5% for the frequency range 20-80 Hz, and is less than 4% in the frequency range of 5-20 Hz when p=-10 is used.) (3) Digital Integrator type V/Hz relaying can be used either for a fixed sampling frequency or for a varying sampling frequency digital protection system. (When the varying sampling frequency approach is used, the coefficients "a" and "b" can be recomputed on-line every time the sampling frequency is changed. In a fixed sampling frequency approach, on the other hand, both "a" and "b" are constants.) (4) The design method described herein ensures that the Digital Integrator is always stable. (5) A Digital Integrator is easy to implement in a digital protection system.

Although exemplary embodiments of the invention have been described in detail above, those skilled in the art will readily appreciate that many additional modifications are possible in the exemplary embodiment without materially departing from the novel teachings and advantages of the invention. For example, those skilled in the art will appreciate that the peak detection method of the invention may employ various other additional steps in addition to those described above. Further, the peak detection system may be used in numerous other systems besides a digital relay system as described herein. Accordingly, all such modifications are intended to be included within the scope of this invention as defined in the following claims. 

What we claim is:
 1. A method of detecting a peak in a sinusoidal digital signal, comprising the steps of:establishing a first threshold which is a first predetermined percentage of the magnitude of the sinusoidal digital signal; establishing a second threshold which is a second predetermined percentage of the magnitude of the sinusoidal digital signal, the second threshold being greater than said first threshold; counting each successive sample in a half-cycle of the sinusoidal digital signal having a magnitude above said first threshold; determining which sample k counted in said counting step had the greatest magnitude, where k is the value for successive samples above the first threshold; comparing a magnitude of sample k to said second threshold; and rejecting said compared sample k as the peak of the sinusoidal digital signal if the magnitude of said sample k is less than said second threshold.
 2. A method as in claim 1, wherein if the magnitude of sample k is greater than the second threshold in said magnitude comparing step, saving the magnitude of sample k as a valid peak value.
 3. A method as in claim 2, comprising the further step of averaging said valid peak value with a last valid peak value of a previous half-cycle of the sinusoidal digital signal.
 4. A method as in claim 3, wherein said first threshold is at a level which is approximately 10-30% of the magnitude of the last valid peak value of the previous half-cycle of the sinusoidal digital signal and the second threshold is at a level which is approximately 40-60% of the magnitude of the last valid peak value of the previous half-cycle of the sinusoidal digital signal.
 5. A method as in claim 4 comprising the further step of updating the levels of said first and second thresholds for each new valid peak value.
 6. A peak detector which detects a peak in a sinusoidal digital signal, comprising:a first threshold which is a first predetermined percentage of the magnitude of the sinusoidal digital signal; a second threshold which is a second predetermined percentage of the magnitude of the sinusoidal digital signal, the second threshold being greater than said first threshold; a counter which counts each successive sample in a half-cycle of the sinusoidal digital signal having a magnitude above said first threshold; and processing means for determining which sample k counted by said counter had the greatest magnitude for comparing a magnitude of sample k to said second threshold, where k is the value for successive samples above the first threshold, and rejecting said compared sample k as the peak of the sinusoidal digital signal if the magnitude of said compared sample k is less than said second threshold.
 7. A peak detector as in claim 6, wherein if said processing means determines that the magnitude of sample k is greater than the second threshold, said processing means saves the magnitude of sample k as a valid peak value.
 8. A peak detector as in claim 7, wherein said processing means averages said valid peak value with a last valid peak value of a previous half-cycle of the sinusoidal digital signal.
 9. A peak detector as in claim 8, wherein said first threshold is at a level which is approximately 10-30% of the magnitude of the last valid peak value of the previous half-cycle of the sinusoidal digital signal and the second threshold is at a level which is approximately 40-60% of the magnitude of the last valid peak value of the previous half-cycle of the sinusoidal digital signal.
 10. A peak detector as in claim 9 wherein said processing means updates the levels of said first and second thresholds for each new valid peak value.
 11. A method of protecting power equipment, supplied with energy from at least one power line, against a source of overexcitation, comprising the steps of:sensing a voltage of said at least one power line; sampling and digitizing said sensed voltage at a sampling frequency so as to form a digital voltage signal; digitally integrating said digital voltage signal independently of said sampling frequency; calculating a peak magnitude of each half-cycle of said digital voltage signal by performing the steps of:accepting only points in said half-cycle having magnitudes above a first threshold, determining a peak magnitude for those points in said half-cycle having magnitudes above said first threshold, and accepting said peak magnitude as a valid peak magnitude if said peak magnitude exceeds a second threshold, greater than said first threshold; and processing said peak magnitude to generate an overexcitation relay signal.
 12. A method as in claim 11, comprising the further step of determining a frequency of said sensed voltage of said at least one power line, wherein said peak magnitude processing step comprises the steps of:calculating a voltage/frequency ratio of said at least one power line from said valid peak magnitude and said frequency determined in said frequency determining step; generating said overexcitation relay signal when said voltage/frequency ratio exceeds a predetermined operating condition value; and providing said overexcitation relay signal to a circuit breaker which separates said power equipment from the source of overexcitation.
 13. A programmed protective relay system for protecting power equipment, supplied with energy from at least one power line, against overexcitation by generating an overexcitation relay signal and providing said overexcitation relay signal to a circuit breaker which separates said power equipment from a source of said overexcitation, said system comprising:a voltage sensor for sensing a voltage of said at least one power line; an analog to digital converter which samples and digitizes said sensed voltage at a sampling frequency so as to form a digital voltage signal; a digital integrator which integrates said digital voltage signal independently of said sampling frequency; a digital rectifier which digitally rectifies said integrated digital voltage signal; and processing means for calculating a peak magnitude of each half-cycle of said rectified digital voltage signal by accepting only points in said half-cycle having magnitudes above a first threshold, determining a peak magnitude for those points in said half-cycle having magnitudes above said first threshold, accepting said peak magnitude as a valid peak magnitude if said peak magnitude exceeds a second threshold, greater than said first threshold, and processing said peak magnitude to generate said overexcitation relay signal.
 14. A system as in claim 13, further comprising frequency determining means for determining a frequency of said sensed voltage of said at least one power line, and wherein said processing means further calculates a voltage/frequency ratio of said at least one power line from said valid peak magnitude and said frequency determined by said frequency determining means and generating said overexcitation relay signal when said voltage/frequency ratio exceeds a predetermined operating condition value. 